Field-induced localization in Fibonacci and Thue-Morse lattices

Abstract

We have undertaken a study of the propagation of carriers in one-dimensional (1D) aperiodic systems within the tight-binding scheme under the action of electric fields. We have concentrated on the Fibonacci (F) and Thue-Morse (TM) lattices, which are of great practical importance since these structures can be fabricated thanks to recent technological advances. We show that superdiffusion takes place for both lattices in the field-free case. The mean-square displacement (MSD) follows the law 〈${\mathit{n}}^{2}$〉\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{\alpha}}}$ with \ensuremath{\alpha}=1.55 for the F lattice and \ensuremath{\alpha}=1.65 for the TM lattice. When the field is included, the particle localizes, i.e., the MSD is bound, even for weak field intensities.